Symmetric solutions of the singular minimal surface equation
type: Item
instance of: scholarly article
title: Symmetric solutions of the singular minimal surface equation
zbMATH Open document ID: 1470.49067
author: Ulrich Dierkes
author: Nico Groh
published in: Annals of Global Analysis and Geometry
publication date: 2021-07-28T00:00:00Z
review text: This nice paper investigates all rotational symmetric solutions \(u\) on a give open set \(\Omega\subset\mathbb R^n\) to the symmetric minimal surface equation \[ \hbox{div}\Bigg(\frac{Du}{\sqrt{1+|Du|^2}}\Bigg)=\frac{\alpha}{u\sqrt{1+|Du|^2}} \] Since the case \(\alpha=0\) of the last equation is the classical minimal surface equation, the results obtained in this paper are classified according to \(\alpha<0\) (Theorem 1) and \(\alpha>0\) (Theorem 7). Moreover, some interesting geometric-analytic properties of the solutions are presented in Theorems 13, 14, 17, 19, 20.
reviewed by: Jie Xiao
Mathematics Subject Classification ID: 49Q05
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 7375620
zbMATH Keywords: singular minimal surface equation
zbMATH Keywords: symmetric solutions
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: s10455-021-09785-2
OpenAlex ID: W3175845938
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DOI: 10.1007/S10455-021-09785-2
description: scientific article; zbMATH DE number 7375620